Let's break down the problem:

We are given the following information:

• A packet of grass seed covers 50 m² of lawn.
• The lawn is circular with a diameter of 20 meters.

Step 1: Calculate the area of the circular lawn

The formula for the area $A$ of a circle is: $A = \pi r^2$ where $r$ is the radius of the circle. The radius is half the diameter, so: $r = \frac{20}{2} = 10 \, \text{meters}$ Now, using the formula for the area: $A = \pi \times (10)^2 = 100 \pi \, \text{square meters}$ $A \approx 100 \times 3.1416 = 314.16 \, \text{m²}$

Step 2: Determine the number of seed packets needed

Since one packet covers 50 m², the number of packets required is: $\text{Packets needed} = \frac{\text{Total area of lawn}}{\text{Area covered by one packet}} = \frac{314.16}{50} \approx 6.28$ Since you can't buy a fraction of a packet, you will need to round up to the nearest whole number, so you need 7 packets.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. What would be the number of packets if the diameter was doubled?
2. How many square meters can 3 packets of grass seed cover?
3. What is the cost if each packet of seed costs $5?
4. How does the area change if the radius is increased by 5 meters?
5. What would be the area if the lawn were an ellipse instead of a circle?

Tip: When solving problems involving areas of circles, remember that the area grows with the square of the radius, so small increases in radius lead to much larger areas.